Effects of the Tsallis distribution in the linear sigma model

Abstract

The effects of the Tsallis distribution which has two parameters, [Formula: see text] and [Formula: see text], on physical quantities are studied using the linear sigma model in chiral phase transitions. The Tsallis distribution approaches the Boltzmann–Gibbs distribution as [Formula: see text] approaches one. The parameter [Formula: see text] dependences of the condensate and mass for various [Formula: see text] are shown, where [Formula: see text] is called temperature. The critical temperature and energy density are described with digamma function, and the [Formula: see text] dependences of these quantities and the extension of Stefan–Boltzmann limit of the energy density are shown. The following facts are clarified. The chiral symmetry restoration at [Formula: see text] occurs at low temperature, compared with the restoration at [Formula: see text]. The sigma mass and pion mass reflect the restoration. The critical temperature decreases monotonically as [Formula: see text] increases. The small deviation from the Boltzmann–Gibbs distribution results in the large deviations of physical quantities, especially the energy density. It is displayed from the energetic point of view that the small deviation from the Boltzmann–Gibbs distribution is realized for [Formula: see text]. The physical quantities are affected by the Tsallis distribution even when [Formula: see text] is small.